Rich,
Ok ive modelled your projectile in 3D CAD as per your dimensions... it came out at 262grains. You didnt give me all the dimensions so i made a few small assumptions such as a jacket thickness of 0.020" etc
These are the principal moments of inertia for your complete projectile, taking into account the aluminium tip, core material and jacket in their relative locations- sorry i live in a metric country
Ix (axial) = 1.1166 g.cm^2
Iy (transverse) = 18.926 g.cm^2
Ky = (radii of gyration) = 10.540mm
Now the only other variable we need to know is the Cma or pitching moment derivative. There is only 2 ways to get an accurate number for this. 1 is live testing in wind tunnels or ballistics range with doppler radar etc, the other is with advanced CFD modelling- neither of which i can help you with. However, we can make some reasonably good assumptions based on the McDrag work done by Robert McCoy. Using his formulas and stability equations, we can assume a Cma of about 4.6 for your projectile aerodynamic geometry. - This is a higher than usual number due to the extreme length of your projectile.
So using the above numbers, i calculate a stability factor as follows, assuming velocity of mach 2.5 (~2850fps) and std atmosphere and temp at sea level.
Sg,
from a 1:8 twist = 1.61
from a 1:9 twist = 1.27
from a 1:10 twist = 1.02 - will most likely tumble.
So the ideal twist rate at sea level is 1:8.3 for an Sg of 1.49.
Take it upto 5000ft, and your ideal twist rate is 1:9 for a 1.47 stability factor.
Take it upto 9000ft, and a 10 twist will work just fine
So a 1:9 will work ok with an Sg of 1.27. Its a little lower than ideal and you may notice some slightly poorer accuracy at short range under 300yds, but it should be ok other than that.
Ok ive modelled your projectile in 3D CAD as per your dimensions... it came out at 262grains. You didnt give me all the dimensions so i made a few small assumptions such as a jacket thickness of 0.020" etc
These are the principal moments of inertia for your complete projectile, taking into account the aluminium tip, core material and jacket in their relative locations- sorry i live in a metric country
Ix (axial) = 1.1166 g.cm^2
Iy (transverse) = 18.926 g.cm^2
Ky = (radii of gyration) = 10.540mm
Now the only other variable we need to know is the Cma or pitching moment derivative. There is only 2 ways to get an accurate number for this. 1 is live testing in wind tunnels or ballistics range with doppler radar etc, the other is with advanced CFD modelling- neither of which i can help you with. However, we can make some reasonably good assumptions based on the McDrag work done by Robert McCoy. Using his formulas and stability equations, we can assume a Cma of about 4.6 for your projectile aerodynamic geometry. - This is a higher than usual number due to the extreme length of your projectile.
So using the above numbers, i calculate a stability factor as follows, assuming velocity of mach 2.5 (~2850fps) and std atmosphere and temp at sea level.
Sg,
from a 1:8 twist = 1.61
from a 1:9 twist = 1.27
from a 1:10 twist = 1.02 - will most likely tumble.
So the ideal twist rate at sea level is 1:8.3 for an Sg of 1.49.
Take it upto 5000ft, and your ideal twist rate is 1:9 for a 1.47 stability factor.
Take it upto 9000ft, and a 10 twist will work just fine
So a 1:9 will work ok with an Sg of 1.27. Its a little lower than ideal and you may notice some slightly poorer accuracy at short range under 300yds, but it should be ok other than that.
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